The answer can be seen if you look at the Contents page of this novel, which lays out the chapters and the novel's structure. Alvarez chooses to structure this wonderful account of the life of the Mirabel sisters by dividing the novel into three parts and giving each sister her "say" in each part. The first sister who starts off each section is of course the one who survived, Dede, who starts off the narrative in the present before retreating into the past. This helps give the novel structure and in addition keeps us focused on the Mirabel sisters as historical figures who continue to "live" metaphorically in the lives and imaginations of so many people as symbols of freedom, power and defiance.
In addition, it also allows Alvarez to paint a compelling portrait of Dede and how she responds to being the one surviving Alvarez sister. She is presented as craving anonymity and dreading the attention that her status gives her:
Oh dear, another one. Now after thirty-four years, the commemorations and interviews and presentations of posthumous honours have almost stopped, so that for months at a time Dede is able to take up her own life again.
Giving us Dede's account of the present and what has happened since the Mirabels' death gives the novel context and allows us to see how their death was not in vain, as well as portraying a fascinating portrait of Dede.